$A$ solid cylinder has a total surface area of $462 \, cm^2$. Its curved surface area is $\frac{1}{3}$ of its total surface area. The volume of the cylinder is.......$cm^3$.

Marbles of diameter $1.4\, cm$ are dropped into a cylindrical beaker containing some water and are fully submerged. The diameter of the beaker is $7\, cm.$ Find how many marbles have been dropped in it if the water rises by $5.6\, cm.$

$A$ cone and a cylinder having the same area of the base have also the same area of curved surfaces. If the height of the cylinder is $2 \, m$,find the slant height of the cone (in $m$).

$A$ cube of edge $3\, cm$ of iron weighs $12\, gm$. What is the weight of a similar cube of iron whose edge is $12\, cm$? (in $gm$)

The areas of three consecutive faces of a cuboid are $12 \, cm^2$,$20 \, cm^2$,and $15 \, cm^2$. Then the volume (in $cm^3$) of the cuboid is:

$A$ solid piece of iron of dimensions $49 \times 33 \times 24 \text{ cm}$ is moulded into a sphere. The radius of the sphere is......$\text{cm}$.